Geodesic
On contiguity relations for generalized hypergeometric functions
Problemy analiza, Tome 7 (2018) no. 2, pp. 39-46.

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We derive formulas that generalize contiguity relations of Gauss hypergeometric functions to the case of hypergeometric functions satisfying differential equations of arbitrary order and also of solution matrices of their corresponding homogeneous differential equations.
Keywords: generalized hypergeometric functions, contiguous functions, Siegel's method. 
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V. A. Gorelov. On contiguity relations for generalized hypergeometric functions. Problemy analiza, Tome 7 (2018) no. 2, pp. 39-46. http://geodesic.mathdoc.fr/item/PA_2018_7_2_a2/

[1] Andrews G., Askey R., Roy R., Special Functions, Cambridge University Press, 2000 ; MCNMO, M., 2013 | MR | Zbl

[2] Bateman H., Erdélyi A., Higher transcendental functions, v. 1, The hypergeometric function, Legendre functions, McGraw-Hill, New York–Toronto–London, 1953; Nauka, M., 1965 | Zbl

[3] Beukers F., Brownawell W. D., Heckman G., “Siegel normality”, Annals of Math., 127, 1988, 279–308 | DOI | MR | Zbl

[4] Bytev V. V., Kalmykov M. Yu., Kniehl B. A., “HYPERDIRE, HYPERgeometric functions DIfferential REduction: MATHEMATICA-based packages for differential reduction of generalized hypergeometric functions ${}_{p}F_{p-1},\,F_1,\,F_2,\,F_3,\,F_4$”, Computer Physics Communications, 184 (2013), 2332–2342 | DOI | MR

[5] Gorelov V. A., “On the algebraic independence of values of generalized hypergeometric functions”, Mathematical Notes, 94:1 (2013), 82–95 | DOI | MR | Zbl

[6] Luke Y., Mathematical functions and their approximations, Academic Press, New York, 1975 ; Mir, M., 1980 | MR | Zbl | Zbl

[7] Salikhov V. Kh., “Formal solutions of linear differential equations and their application in the theory of transcendental numbers”, Trans. Moscow Math. Soc., 1989, 219–251 | MR | Zbl

[8] Shidlovskii A. B., Transcendental numbers, Nauka, M., 1987 ; Walter de Gruyter, Berlin–New York, 1989 | MR | Zbl

[9] Slater L. J., Generalized Hypergeometric Functions, Cambridge University Press, London–New York, 1966 | MR | Zbl

[10] Viskina G. G., Salikhov V. Kh., “Algebraic relations between hypergeometric E-function and its derivatives”, Mathematical Notes, 71:6 (2002), 761–772 | DOI | MR | Zbl